|MadSci Network: Physics|
There are two things involved in the temperature reached in an explosion. The first one involves the concept of limits. When a volcanic eruption takes place, hot magma and gases are released into the atmosphere, and it can be pretty spectacular. But, the energy release results from essentially stored energy, in part due to gases being trapped underground at high pressure. There is no chemical or nuclear reaction taking place that would increase the temperature of the magma or gases. So, if you have magma and gases stored underground at around 1,200C, the melting point of the magma, then that is the maximum temperature that you will see in a volcanic-based explosion. Even magma directly in contact with the outer core of the earth's mantle is apparently only 3,700C, according to this reference: http://www.sciencedaily.com/releases/2007/04/070406171041.htm So, at its limits, a volcanic eruption can only release material at the highest temperature that it is stored at. If the magma started at 1,200C, then a volcanic explosion will not produce temperatures of any materials that exceed 1,200C. (There might be some small chemical reactions that take place when the magma hits the air, but it shouldn't change the situation much, especially considering the masses involved, which gets us to the second concept.) With a nuclear or chemical explosion, energy is being released as a result of a nuclear or chemical reaction. A nuclear explosion releases a certain amount of energy for every nuclear reaction. In other words, every time an atom undergoes fission or fusion, it releases a set amount of energy. Similarly in a chemical reaction, every time an oxygen molecule reacts with a hydrocarbon to produce water and carbon dioxide, a certain amount of energy is released. In this case, the energy released is not based upon the initial temperature of whatever is reacting. With a candle flame, for example (you might think of it as a very, very slow chemical explosion), oxygen reacts with the hydrocarbon fuel to make water vapor and carbon dioxide. In the process, nitrogen mixed in with the oxygen in the air also gets heated up, so the temperature of a candle flame is about 1,400C at its peak. (Gaydon, A. G., and Wolfhard, H. G., Flames: Their Structure, Radiation and Temperature, 3rd ed., Chapman and Hall, London (1970)). Even if I build a bigger fire, the temperature still isn't going to increase much, because the mass of the water vapor, carbon dioxide, and nitrogen still remain in the same proportion to the amount of heat given off. We can reduce the amount of mass being heated by a candle flame by feeding pure oxygen to the flame, rather than air. Now, the products carrying away heat from the reaction are just the water vapor and carbon dioxide (no nitrogen). As a result, the flame temperature would increase several hundred degrees. In a nuclear explosion, there are a very large number of nuclear events happening in a short time, each tiny event adding a specific amount of energy. All that energy that is released can only do three things, given the small amount of time available. Energy can be directly released as light and x-rays. The energy can be used to heat up the bomb materials, and the energy can be used to push the bomb and surrounding air out of the way, forming a blast wave. The bomb itself is relatively small in mass; let's say the bomb only weighs 200 kg. The specific heat of the bomb materials are maybe similar to uranium, which has a specific heat of 0.12J/gK, a heat of fusion of 8.52 kJ/mole, and a heat of vaporization of 477 kJ/mole. (see http://www.chemicool.com/elements/uranium.html) So, to heat one mole of a uranium bomb at 4203K will require 3930K*0.12J/gK*238g/mole= 112240J plus 8520J to melt it + 477000J to vaporize it, or about 600,000J per mole. So to vaporize the entire bomb of 840 moles of uranium is only going to take about 504 * 10^6 joules, and the bomb is producing 4 * 10^16 joules. So you have about 10 billion times more energy available from the nuclear blast than what is needed to simply vaporize the bomb at about 4000K. No wonder that the temperatures of nuclear explosions reach into the millions of degrees. So the second limit on the temperature of an explosion is related to the amount of mass that is involved or heated by the reaction. In a volcanic explosion, there are millions of tons of mass involved in the eruption, so even if the magma was producing heat through a chemical or nuclear reaction, the temperature of the magma would not change appreciably since the heat of the reaction would have to heat so much material. I hope that answers your question. Thanks for asking.
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